is now considered. This kind of equation appears for instance in the prediction of electron density \(f\)  of the Earth radiation belts and results from a Hamiltonian formalism applied on a typical Boltzmann equation, where a Fokker-Planck operator is introduced to evaluate physical interactions responsible for changing particles trapping state [1]}. In the radiation belts, the typical spatial coordinates system \(x\)  in Eq. (REF ) stands in this case for a combined spatial and physical quantities e.g. the energy of the electrons.
The diffusion equation is also important in the modeling of atmospheric boundary layer where it represents the effect of the turbulence [2]}.
In this example, and by identification with Eq. (REF ), \(f\)  stands for \(\chi \)  while \(\mathcal {M}(f,\partial f)=\partial _x \left(D\partial _x f\right)\) .
